If the interest is compounded half-yearly, calculate the amount when the principal is ₹7400, the rate of interest is 5% and the duration is one year.

Since rate of interest is 5% per annum, therefore rate of interest per conversion period (half-yearly) = 2.5%.

As the money is invested for one year, therefore,

n (the number of conversion periods) = 2.

$\therefore A = P\Big(1 + \dfrac{r}{100}\Big)^n \\[1em] = ₹7400 \times \Big(1 + \dfrac{2.5}{100}\Big)^2 \\[1em] = ₹7400 \times \Big(\dfrac{102.5}{100}\Big)^2 \\[1em] = ₹7400 \times \Big(\dfrac{1025}{1000}\Big)^2 \\[1em] = ₹7400 \times \Big(\dfrac{41}{40}\Big)^2 \\[1em] = ₹7400 \times \dfrac{41}{40} \times \dfrac{41}{40} \\[1em] = ₹ \dfrac{12439400}{1600} \\[1em] = ₹7774.625$

Hence, amount = ₹7774.625